This article is about a professor at University of Pennsylvania, Dennis DeTurck, who claimed that fractions were obsolete and were not useful in society anymore. This was with the exception of cooking and carpentry. I disagree completely, especially after reading the chapters in our book on ratio, proportion and percents. I feel as though students need fractions for more than just cooking and carpentry. It seems a lot easier to use fractions when figuring out problems involving ratios, proportions, and percents. For example, when given a problem comparing ratios, it is easier to use fractions to figure them out than decimals or other methods. I agree with Janine Remillard, associate professor of education at Penn, that if fractions are taught well, kids can actually understand the value of the size of pieces.
As far as long division is concerned, I feel that with the availability of calculators and technology today, long division does not need to be taught as intensely as it is currently taught. I especially think that students who struggle in math could benefit more greatly from learning other aspects of math. I think that teaching the basics of division and estimation can help a student more greatly in solving real life problems.
Sunday, May 2, 2010
Chapter 12: Fractions and Decimals
Fractions can be the most difficult math concept to teach. If done well however, students can get a lot of enjoyment out of fractions and it can be a lot of fun. This chapter described the three meanings of fractions which are part-whole, quotient, and ratio. It is important to begin with teaching fractions as equal parts of a whole. Using concrete models for much of teaching fractions is an important tool in teaching fractions.
I personally like teaching fractions. You can use so many things to show what a fraction is, including pizza, colors in a bag of M&Ms, tiles, pattern blocks…..the list goes on. I think students can get a lot of fun out of fractions.
Adding and subtracting fractions with unlike denominators can be difficult. I like the way the book teaches students how to add and subtract fractions and will definitely use this next time I teach students this concept.
Relating decimals to fractions can be extremely difficult, especially for students with executive functioning issues. It is multi-step and can be hard to teach concretely. What was interesting to me, however, is that different countries teach fractions and decimals at different grade levels.
I personally like teaching fractions. You can use so many things to show what a fraction is, including pizza, colors in a bag of M&Ms, tiles, pattern blocks…..the list goes on. I think students can get a lot of fun out of fractions.
Adding and subtracting fractions with unlike denominators can be difficult. I like the way the book teaches students how to add and subtract fractions and will definitely use this next time I teach students this concept.
Relating decimals to fractions can be extremely difficult, especially for students with executive functioning issues. It is multi-step and can be hard to teach concretely. What was interesting to me, however, is that different countries teach fractions and decimals at different grade levels.
Chapter 14: Algebraic Thinking
Algebra can be difficult to teach. I think the earlier we introduce students to some form of algebra, the better. I like the introduction where the book defines algebra in many different forms. I actually did not know that patterns were a form of algebra. I have always thought of algebra as A+B=C. There is much more to algebra to that and it connects a lot of pieces of math with it. While there is emphasis on finding missing numbers, it does show a lot of different ways to do things.
Algebra is difficult because it can be so abstract. I think students have difficulty with the abstract and teachers have difficulty teaching abstract concepts. I think this is where the breakdown occurs. Students don’t have to just memorize algebraic facts, theories, and concepts. They can learn by doing and the chapter does a really good job of showing that.
Algebra is difficult because it can be so abstract. I think students have difficulty with the abstract and teachers have difficulty teaching abstract concepts. I think this is where the breakdown occurs. Students don’t have to just memorize algebraic facts, theories, and concepts. They can learn by doing and the chapter does a really good job of showing that.
Chapter 13: Ratio, Proportion, and Percent
Chapter 13 begins with some examples of ratios in real life. I think that this is a great way to introduce ratios to children and show them how it is used in real life. I thought that using the sticker to dime example was a great way to show students in elementary school how to use ratios. Using money to show students is a great real life example that students can relate to. I think giving children multiple ways to express a ratio (i.e. fractions, percents) is important to reinforce. Using patterns is another concrete way to show students relationships between two or more things. I think the relationship between fractions and ratios is important to reinforce, but I know that we do not do that enough in our program. I don't think that we show kids that you can combine ratios by adding fractions.
I think that proportions is a difficult concept for students to understand. There are multiple steps involved in comparing two ratios and students need to have a strong understanding of ratios, problem solving, and comparing fractions. These are all difficult concepts for students to understand. Teaching multiple ways to solve problems as in Figure 13-7 might be confusing to children and knowing how the children learn the best is important in this case. It is extremely important to give students real life, concrete examples in the case of proportional reasoning.
Percent may be easier for students to understand. A teacher can use multiple real life examples for students to make a connection to, thus making it easier for them to understand the concept. A student can understand the basic concept of percent just by knowing that it is a ratio based on 100. I agree that students do need to have strong understanding of fractions and decimals in order to understand percents. Multiple discussions around solving percent problems is important because it helps students grasp the concept, especially when using real life examples.
I think that proportions is a difficult concept for students to understand. There are multiple steps involved in comparing two ratios and students need to have a strong understanding of ratios, problem solving, and comparing fractions. These are all difficult concepts for students to understand. Teaching multiple ways to solve problems as in Figure 13-7 might be confusing to children and knowing how the children learn the best is important in this case. It is extremely important to give students real life, concrete examples in the case of proportional reasoning.
Percent may be easier for students to understand. A teacher can use multiple real life examples for students to make a connection to, thus making it easier for them to understand the concept. A student can understand the basic concept of percent just by knowing that it is a ratio based on 100. I agree that students do need to have strong understanding of fractions and decimals in order to understand percents. Multiple discussions around solving percent problems is important because it helps students grasp the concept, especially when using real life examples.
Tuesday, March 16, 2010
Grading What Matters.....
In the article Grading What Matters, the author talks about how teachers are grading based on nonacademic standards rather than when the student is actually learning in the classroom. The article says that students are being graded on responsibility and compliance rather than what the child is actually learning and retaining in the classroom. The article then talks about teachers moving to a different way of grading and shifting their focus to higher-level thinking from compliance and memorization of facts just for a test. The author of the article was saying that you can grade for compliance, but a majority of a students grade should focus on the understanding of the material being taught to them. Separating nonacademic and academic factors in a teachers grade book allows both grading systems to be used. Moving from knowledge (students memorizing information, short-term memory) to understanding (higher order thinking, long term memory) will help students meet academic demands in their future learning.
Coming from a background of teaching at a private school for children with significant behavioral, social and emotional issues, where we do not give grades, it was difficult for me to relate to the article as a teacher. I have not had the opportunity to grade students based on their work handed in, but on their ability to really understand material given to them, using academic assessments and testing. I think this article is really informative, however, and if I have the opportunity in the future to give letter grades to students, I will definitely think of this article and target my grading system based on what the article said. In the long run, using this grading system where students are expected to use a higher level of thinking rather than bull s*%$ing their way through a paper or essay will help them through college and into their careers.
I remember being in middle/high school and getting good grades. Most of how I was assessed was through memorization of facts that I had to regurgitate onto a test. I would memorize what I needed to for the test and once the test was over, I would forget what was even on the test. I feel like the MTEL's are the same for adults. We are expected to remember information from grades K-12, especially with the general curriculum test, but once the test is over, we know we will not use any of the information we just memorized.
Coming from a background of teaching at a private school for children with significant behavioral, social and emotional issues, where we do not give grades, it was difficult for me to relate to the article as a teacher. I have not had the opportunity to grade students based on their work handed in, but on their ability to really understand material given to them, using academic assessments and testing. I think this article is really informative, however, and if I have the opportunity in the future to give letter grades to students, I will definitely think of this article and target my grading system based on what the article said. In the long run, using this grading system where students are expected to use a higher level of thinking rather than bull s*%$ing their way through a paper or essay will help them through college and into their careers.
I remember being in middle/high school and getting good grades. Most of how I was assessed was through memorization of facts that I had to regurgitate onto a test. I would memorize what I needed to for the test and once the test was over, I would forget what was even on the test. I feel like the MTEL's are the same for adults. We are expected to remember information from grades K-12, especially with the general curriculum test, but once the test is over, we know we will not use any of the information we just memorized.
My first class.....
So, this is my first time writing a blog. I am usually uncomfortable with people reading my thoughts or ideas, but I guess it's time to expand my comfort zone.
Last week, class went really well. I like learning through playing games. It beats lecturing off a power point any day. I hope they continue like this through the next seven weeks. It seems like this is going to be an interesting class.
I also like using technology and learning about technology for the purpose of teaching kids today. I know that at our program, we can't afford some technology and look to grants to get what we need, but it will be nice to learn of some free technology that we can use in the classroom.
Anyway, as far as it being kind of a "late night" for us students (we are used to getting out of class around 7:30-8), I thought it was a really enjoyable class and it seems like we are in for some good times and good learning!
Last week, class went really well. I like learning through playing games. It beats lecturing off a power point any day. I hope they continue like this through the next seven weeks. It seems like this is going to be an interesting class.
I also like using technology and learning about technology for the purpose of teaching kids today. I know that at our program, we can't afford some technology and look to grants to get what we need, but it will be nice to learn of some free technology that we can use in the classroom.
Anyway, as far as it being kind of a "late night" for us students (we are used to getting out of class around 7:30-8), I thought it was a really enjoyable class and it seems like we are in for some good times and good learning!
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